Non-reciprocal piezoelectric metamaterials with tunable mode shapes

The mode shapes of piezoelectric metamaterials are tuned by manipulating spatially the electrical boundary conditions of the piezo-elements, in a desired and controlled manner, in order to tailor the wave propagation characteristics through these metamaterials. The boundary conditions of the piezo-elements are controlled by using inductive shunting networks. With appropriate tuning and optimization of the spatial distribution of these inductive boundary conditions, it would be possible to alter the mode shape characteristics of the metamaterial in order to control the magnitude and direction of wave propagation. This enables also breaking the reciprocity characteristics of the metamaterial in a controlled manner. A finite element model (FEM) is developed to model the mode shape characteristics and the wave propagation in a one-dimensional piezo-metamaterial. The effect of various shunting strategies on the spatial control of the mode shapes, energy flow, and reciprocity characteristics of the piezo-metamaterial are investigated. The presented work lays down the foundation for two and three-dimensional metamaterial with tunable mode shape characteristics.